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arXiv:0905.1204 · Journal of Physics B Atomic Molecular and Optical Physics

Off-resonance absorption and dispersion in vapours of hot alkali-metal atoms

Paul Siddons, Charles S. Adams, Ifan G. Hughes

Published Aug 14, 2009• 42 citations
arXivHTMLPDF

Abstract

We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion, and show that dispersion dominates the atom-light interaction far from resonance. The calculated absorption and dispersion are compared to experimental data, showing the validity of the approximations.

DOI
10.1088/0953-4075/42/17/175004

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We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion, and show that dispersion dominates the atom-light interaction far from resonance. The calculated absorption and dispersion are compared to experimental data, showing the validity of the approximations.
Abstract The spectroscopy of hot atomic vapours is a hot topic. Many of the work-horse techniques of contemporary atomic physics were first demonstrated in hot vapours. Alkali-metal atomic vapours are ideal media for quantum-optics experiments as they combine: a large resonant optical depth; long coherence times; and well-understood atom–atom interactions. These features aid with the simplicity of both the experimental set up and the theoretical framework. The topic attracts much attention as these systems are ideal for studying both fundamental physics and has numerous applications, especially in sensing electromagnetic fields and quantum technology. This tutorial reviews the necessary theory to understand the Doppler broadened absorption spectroscopy of alkali-metal atoms, and explains the data taking and processing necessary to compare theory and experiment. The aim is to provide a gentle introduction to novice scientists starting their studies of the spectroscopy of thermal vapours while also calling attention to the application of these ideas in the contemporary literature. In addition, the work of expert practitioners in the field is highlighted, explaining the relevance of three extensively-used software packages that complement the presentation herein.
A detailed theory of the frequency dependence of the electro-optical Kerr effect of an atom in the region of absorption lines is presented and applied to the particular case of 2 P←2 S doublets of sodium and lithium vapours. Doppler broadening is taken into account. With electric dipole matrix elements derived from the Coulomb approximation for both discrete and continuum states, the molar Kerr constant, m K(32 P←32 S), of atomic sodium vapour in the D-line absorption region is calculated to ±30 per cent; the calculations indicate that m K in the vicinity of the D2 line (32 P 3/2←32 S 1/2) should be very much greater than near the D1 line (32 P 1/2←32 S 1/2) in qualitative agreement with the experiments of Kopfermann and Ladenburg Qualitative consideration is also given to dispersion of magnetic birefringence; in contrast with electric birefringence strong dispersion is expected near both lines of alkali metal 2 P←2 S doublets.
The absorptive and dispersive properties of a Doppler-broadened vapour of rubidium atoms is investigated. A detailed model of the atom-light interaction is developed and found to be in excellent agreement with experiment in the regime where the interacting light field is sufficiently weak such that it does not significantly alter the medium through which it propagates. The importance of using a weak beam to probe atomic systems is discussed, and a method of characterising how weak such a beam has to be is provided. The theoretical model is applied to both situations of illumination by continuous-wave and pulsed light, the latter situation providing a demonstration of the slow light effect. This phenomenon is a manifestation of the dispersive properties of the medium and is shown to exist over a particularly large frequency range, compared to the absorption spectrum, in thermal vapours. Off-resonant interactions are studied, in which incident laser-light is detuned from resonance to such a degree that Doppler-broadening can be neglected. We quantify the extent to which the light needs to be detuned to be in this regime, and provide approximations to the line-shape function developed in earlier parts of the thesis. The approximate line-shapes are much easier to manipulate and allow a more intuitive understanding of the atom-light interaction. In the second part of the thesis we study the Faraday effect and related phenomena which are an expression of the birefringent properties of the atom-light system. Beginning with a theoretical and experimental investigation of the Faraday rotation of a weak continuous-wave beam, we move on to the consideration of pulsed light. Optically-induced birefringence via the application of an intense continuous-wave pumping field is demonstrated experimentally, and the theoretical plausibility of controlling the polarisation state of a weak pulsed field mediated via intense pulsed light is shown.
Abstract Laser spectroscopy of hot atomic vapours has been studied extensively. Theoretical models that predict the absolute value of the electric susceptibility are crucial for optimising the design of photonic devices that use hot vapours, and for extracting parameters, such as external fields, when these devices are used as sensors. To date, most of the models developed have been restricted to the weak-probe regime. However, fulfilling the weak-probe power constraint may not always be easy, desired or necessary. Here we present a model for simulating the spectra of alkali-metal vapours for a variety of experimental parameters, most distinctly at intensities beyond weak laser fields. The model incorporates optical pumping effects and transit-time broadening. We test the performance of the model by performing spectroscopy of 87Rb in a magnetic field of 0.6 T, where isolated atomic resonances can be addressed. We find very good agreement between the model and data for three different beam diameters and a variation of intensity of over five orders of magnitude. The non-overlapping absorption lines allow us to differentiate the saturation behaviour of open and closed transitions. While our model was only experimentally verified for the D2 line of rubidium, the software is also capable of simulating spectra of rubidium, sodium, potassium and caesium over both D lines.
This thesis presents a comparative study of the measured and calculated absolute absorption and dispersion properties of the Rb D lines through a dense thermal vapour in the absence and presence of an applied magnetic field. A detailed theoretical model valid in the weak-probe regime is calculated. The model uses a matrix representation of the atomic Hamiltonian including the magnetic field interaction for Rb in the completely uncoupled basis. Numerical diagonalisation allows the frequency detunings and transition strengths to be calculated. The lineshape of each transition is modelled as a Voigt profile, a convolution of the inhomogeneous and homogeneous profiles. The medium’s susceptibility is found by summing over all the electric-dipole-allowed transitions. For dense thermal vapours a modification to the homogeneous linewidth of each transition, which grows linearly with the number density of atoms, arises due to resonant dipole-dipole interactions between identical atoms in superpositions of the ground and excited terms. In the presence of an applied magnetic field we investigate the Stokes parameters of light propagating through a dense thermal vapour. For fields larger than 0.33 T we enter the hyperfine Paschen-Back regime on the Rb D lines. We present a compact optical isolator based on an atomic vapour, exploiting the spectral region of high transmission and large dispersion where we would normally expect absorption on the Rb D lines. Frequency up-conversion is shown in the fluorescence measurements over the visible and near infra-red regions for strong excitation. Low density transfer arises due to the energy-pooling effect between two identical atoms in their first excited terms. At high densities resonant dipole-dipole interactions give rise to a threshold for the energy transfer. We characterise the threshold behaviour with increasing number density.
We investigate the influence of Doppler broadening on absorption-dispersion properties in a four-level atomic system that can evolve from a normal dispersion to an anomalous dispersion. Our results show that the absorption-dispersion properties become strongly dependent on the propagation directions of the applied fields if Doppler broadening is taken into account. Especially, the switchover in the sign of the dispersion is still achievable even in the presence of Doppler broadening if properly arranging the propagation directions of the applied fields, which is in contrast with the otherwise behaviours in some other configurations.